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Simplifying 307.5 = 0.04(v2) + 1.1(v) Reorder the terms: 307.5 = 1.1v + 0.04v2 Solving 307.5 = 1.1v + 0.04v2 Solving for variable 'v'. Reorder the terms: 307.5 + -1.1v + -0.04v2 = 1.1v + -1.1v + 0.04v2 + -0.04v2 Combine like terms: 1.1v + -1.1v = 0.0 307.5 + -1.1v + -0.04v2 = 0.0 + 0.04v2 + -0.04v2 307.5 + -1.1v + -0.04v2 = 0.04v2 + -0.04v2 Combine like terms: 0.04v2 + -0.04v2 = 0.00 307.5 + -1.1v + -0.04v2 = 0.00 Begin completing the square. Divide all terms by -0.04 the coefficient of the squared term: Divide each side by '-0.04'. -7687.5 + 27.5v + v2 = 0 Move the constant term to the right: Add '7687.5' to each side of the equation. -7687.5 + 27.5v + 7687.5 + v2 = 0 + 7687.5 Reorder the terms: -7687.5 + 7687.5 + 27.5v + v2 = 0 + 7687.5 Combine like terms: -7687.5 + 7687.5 = 0.0 0.0 + 27.5v + v2 = 0 + 7687.5 27.5v + v2 = 0 + 7687.5 Combine like terms: 0 + 7687.5 = 7687.5 27.5v + v2 = 7687.5 The v term is 27.5v. Take half its coefficient (13.75). Square it (189.0625) and add it to both sides. Add '189.0625' to each side of the equation. 27.5v + 189.0625 + v2 = 7687.5 + 189.0625 Reorder the terms: 189.0625 + 27.5v + v2 = 7687.5 + 189.0625 Combine like terms: 7687.5 + 189.0625 = 7876.5625 189.0625 + 27.5v + v2 = 7876.5625 Factor a perfect square on the left side: (v + 13.75)(v + 13.75) = 7876.5625 Calculate the square root of the right side: 88.75 Break this problem into two subproblems by setting (v + 13.75) equal to 88.75 and -88.75.Subproblem 1
v + 13.75 = 88.75 Simplifying v + 13.75 = 88.75 Reorder the terms: 13.75 + v = 88.75 Solving 13.75 + v = 88.75 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-13.75' to each side of the equation. 13.75 + -13.75 + v = 88.75 + -13.75 Combine like terms: 13.75 + -13.75 = 0.00 0.00 + v = 88.75 + -13.75 v = 88.75 + -13.75 Combine like terms: 88.75 + -13.75 = 75 v = 75 Simplifying v = 75Subproblem 2
v + 13.75 = -88.75 Simplifying v + 13.75 = -88.75 Reorder the terms: 13.75 + v = -88.75 Solving 13.75 + v = -88.75 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-13.75' to each side of the equation. 13.75 + -13.75 + v = -88.75 + -13.75 Combine like terms: 13.75 + -13.75 = 0.00 0.00 + v = -88.75 + -13.75 v = -88.75 + -13.75 Combine like terms: -88.75 + -13.75 = -102.5 v = -102.5 Simplifying v = -102.5Solution
The solution to the problem is based on the solutions from the subproblems. v = {75, -102.5}
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